When you add integers, why do you subtract? -9+5=-4. I do not understand why there is an addition sign. How do you know when you are suppose to subtract.
Let's suppose you owe someone $9.00 (-9). You pay him $5.00 (+5). You'll still owe him $4.00 (-4).
This integer line may also help you visualize this problem.
http://education.smarttech.com/NR/rdonlyres/98A932F3-0E77-4C02-ADD0-04D9975ACDEA/0/NumberlineIntegers.gif
When adding integers, you are correct that you generally use the addition operation. However, when dealing with negative numbers, it may seem counterintuitive that you sometimes need to subtract.
To understand why we subtract in certain cases, we can think of adding a negative number as subtracting the corresponding positive number.
For example, let's consider the problem -9 + 5.
Step 1: Start with the first number, which is -9.
Step 2: Since we have a positive number after the plus sign, we need to add it. In this case, we add 5.
Step 3: However, since we are adding a negative number (because 5 is a positive number here, but we are adding it to a negative number), we can think of it as subtracting the corresponding positive number. So, subtract 5.
So, -9 + 5 can be thought of as -9 - 5, which equals -14.
To summarize, when you have a positive number after the plus sign, you add it as usual. But when you have a negative number, you can think of it as subtracting the corresponding positive number.
When determining whether to add or subtract, you can remember these rules:
- If you have two positive numbers, add them.
- If you have two negative numbers, add them.
- If you have one positive and one negative number, subtract the smaller absolute value from the larger absolute value, and use the sign of the number with the larger absolute value.
I hope this explanation helps clarify why we subtract when adding integers with negative numbers!